421 research outputs found
A stable FSI algorithm for light rigid bodies in compressible flow
In this article we describe a stable partitioned algorithm that overcomes the
added mass instability arising in fluid-structure interactions of light rigid
bodies and inviscid compressible flow. The new algorithm is stable even for
bodies with zero mass and zero moments of inertia. The approach is based on a
local characteristic projection of the force on the rigid body and is a natural
extension of the recently developed algorithm for coupling compressible flow
and deformable bodies. Normal mode analysis is used to prove the stability of
the approximation for a one-dimensional model problem and numerical
computations confirm these results. In multiple space dimensions the approach
naturally reveals the form of the added mass tensors in the equations governing
the motion of the rigid body. These tensors, which depend on certain surface
integrals of the fluid impedance, couple the translational and angular
velocities of the body. Numerical results in two space dimensions, based on the
use of moving overlapping grids and adaptive mesh refinement, demonstrate the
behavior and efficacy of the new scheme. These results include the simulation
of the difficult problem of a shock impacting an ellipse of zero mass.Comment: 32 pages, 20 figure
Homogeneous links, Seifert surfaces, digraphs and the reduced Alexander polynomial
We give a geometric proof of the following result of Juhasz. \emph{Let
be the leading coefficient of the Alexander polynomial of an alternating knot
. If then has a unique minimal genus Seifert surface.} In
doing so, we are able to generalise the result, replacing `minimal genus' with
`incompressible' and `alternating' with `homogeneous'. We also examine the
implications of our proof for alternating links in general.Comment: 37 pages, 28 figures; v2 Main results generalised from alternating
links to homogeneous links. Title change
Fine-structure constant variability, equivalence principle and cosmology
It has been widely believed that variability of the fine-structure constant
alpha would imply detectable violations of the weak equivalence principle. This
belief is not justified in general. It is put to rest here in the context of
the general framework for alpha variability [J. D. Bekenstein, Phys. Rev. D 25,
1527 (1982)] in which the exponent of a scalar field plays the role of the
permittivity and inverse permeability of the vacuum. The coupling of particles
to the scalar field is necessarily such that the anomalous force acting on a
charged particle by virtue of its mass's dependence on the scalar field is
cancelled by terms modifying the usual Coulomb force. As a consequence a
particle's acceleration in external fields depends only on its charge to mass
ratio, in accordance with the principle. And the center of mass acceleration of
a composite object can be proved to be independent of the object's internal
constitution, as the weak equivalence principle requires. Likewise the widely
employed assumption that the Coulomb energy of matter is the principal source
of the scalar field proves wrong; Coulomb energy effectively cancels out in the
continuum description of the scalar field's dynamics. This cancellation
resolves a cosmological conundrum: with Coulomb energy as source of the scalar
field, the framework would predict a decrease of alpha with cosmological
expansion, whereas an increase is claimed to be observed. Because of the said
cancellation, magnetic energy of cosmological baryonic matter is the main
source of the scalar field. Consequently the expansion is accompanied by an
increase in alpha; for reasonable values of the framework's sole parameter,
this occurs at a rate consistent with the observers' claims.Comment: RevTeX-4, 22 pages, no figures, added a section on caveats as well as
several new references with discussion of them in body. To appear in Phys.
Rev.
Stabilization of internal spaces in multidimensional cosmology
Effective 4-dimensional theories are investigated which were obtained under
dimensional reduction of multidimensional cosmological models with a minimal
coupled scalar field as matter source. Conditions for the internal space
stabilization are considered and the possibility for inflation in the external
space is discussed. The electroweak as well as the Planck fundamental scale
approaches are investigated and compared with each other. It is shown that
there exists a rescaling for the effective cosmological constant as well as for
gravitational exciton masses in the different approaches.Comment: 12 pages, LaTeX2e, to appear in Phys.Rev.D, note adde
Non-Commutative Inflation
We show how a radiation dominated universe subject to space-time quantization
may give rise to inflation as the radiation temperature exceeds the Planck
temperature. We consider dispersion relations with a maximal momentum (i.e. a
mimimum Compton wavelength, or quantum of space), noting that some of these
lead to a trans-Planckian branch where energy increases with decreasing
momenta. This feature translates into negative radiation pressure and, in
well-defined circumstances, into an inflationary equation of state. We thus
realize the inflationary scenario without the aid of an inflaton field. As the
radiation cools down below the Planck temperature, inflation gracefully exits
into a standard Big Bang universe, dispensing with a period of reheating.
Thermal fluctuations in the radiation bath will in this case generate curvature
fluctuations on cosmological scales whose amplitude and spectrum can be tuned
to agree with observations.Comment: 4 pages, 3 figure
Shape Dynamics in 2+1 Dimensions
Shape Dynamics is a formulation of General Relativity where refoliation
invariance is traded for local spatial conformal invariance. In this paper we
explicitly construct Shape Dynamics for a torus universe in 2+1 dimensions
through a linking gauge theory that ensures dynamical equivalence with General
Relativity. The Hamiltonian we obtain is formally a reduced phase space
Hamiltonian. The construction of the Shape Dynamics Hamiltonian on higher genus
surfaces is not explicitly possible, but we give an explicit expansion of the
Shape Dynamics Hamiltonian for large CMC volume. The fact that all local
constraints are linear in momenta allows us to quantize these explicitly, and
the quantization problem for Shape Dynamics turns out to be equivalent to
reduced phase space quantization. We consider the large CMC-volume asymptotics
of conformal transformations of the wave function. We then use the similarity
of Shape Dynamics on the 2-torus with the explicitly constructible strong
gravity (BKL) Shape Dynamics Hamiltonian in higher dimensions to suggest a
quantization strategy for Shape Dynamics.Comment: 15 pages, LaTeX, no figure
Instantons, the QCD Vacuum, and Hadronic Physics
A large body of evidence from lattice calculations indicates that instantons
play a major role in the physics of light hadrons. This evidence is summarized,
and recent results concerning the instanton content of the SU(3) vacuum,
instanton contributions to the static potential, and a new class of instanton
solutions at finite temperature are reviewed.Comment: 13 pages, 8 figures, Latex using Boxed EPS Macros, LATTICE98 Plenary
Tal
Noncommutative Self-dual Gravity
Starting from a self-dual formulation of gravity, we obtain a noncommutative
theory of pure Einstein theory in four dimensions. In order to do that, we use
Seiberg-Witten map. It is shown that the noncommutative torsion constraint is
solved by the vanishing of commutative torsion. Finally, the noncommutative
corrections to the action are computed up to second order.Comment: 15+1 pages, LaTeX, no figure
Exact Black Holes and Gravitational Shockwaves on Codimension-2 Branes
We derive exact gravitational fields of a black hole and a relativistic
particle stuck on a codimension-2 brane in dimensions when gravity is ruled
by the bulk -dimensional Einstein-Hilbert action. The black hole is locally
the higher-dimensional Schwarzschild solution, which is threaded by a tensional
brane yielding a deficit angle and includes the first explicit example of a
`small' black hole on a tensional 3-brane. The shockwaves allow us to study the
large distance limits of gravity on codimension-2 branes. In an infinite
locally flat bulk, they extinguish as , i.e. as on a 3-brane
in , manifestly displaying the full dimensionality of spacetime. We check
that when we compactify the bulk, this special case correctly reduces to the 4D
Aichelburg-Sexl solution at large distances. Our examples show that gravity
does not really obstruct having general matter stress-energy on codimension-2
branes, although its mathematical description may be more involved.Comment: 18 pages, LaTeX; v2: added references, version to appear in JHE
Dynamics of Phase Transitions by Hysteresis Methods I
In studies of the QCD deconfining phase transition or crossover by means of
heavy ion experiments, one ought to be concerned about non-equilibrium effects
due to heating and cooling of the system. Motivated by this, we look at
hysteresis methods to study the dynamics of phase transitions. Our systems are
temperature driven through the phase transition using updating procedures in
the Glauber universality class. Hysteresis calculations are presented for a
number of observables, including the (internal) energy, properties of
Fortuin-Kasteleyn clusters and structure functions. We test the methods for 2d
Potts models, which provide a rich collection of phase transitions with a
number of rigorously known properties. Comparing with equilibrium
configurations we find a scenario where the dynamics of the transition leads to
a spinodal decomposition which dominates the statistical properties of the
configurations. One may expect an enhancement of low energy gluon production
due to spinodal decomposition of the Polyakov loops, if such a scenario is
realized by nature.Comment: 12 pages, revised after referee report, to appear in Phys. Rev.
- …